Pairwise Marginal Likelihood for the Bradley-Terry Model
The statistical inference for the Bradley-Terry model with logit link and random effects is often made cumbersome by the high-dimensional intractable integrals involved in the marginal likelihood. An inferential methodology based on the marginal pairwise likelihood approach is proposed. This method belongs to the broad class of composite likelihood and involves marginal pairs probabilities of the responses. These probabilities are derived from the approximation of the logistic distribution function by a normal scale mixture. The sample performance of this approach is evaluated by a simulation study. The main motivation of this work is the lizards data, on which the the proposed approach is illustrated.
KeywordsBradley-Terry model Composite likelihood Fixed effects Lizards data Logit link Marginal pairwise likelihood Marginal maximum likelihood Probit link Variance component
AMS Subject Classification62F12 62H12 62J02 62J12 62J15
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